Inaug.-Diss.--Munich, 1967. / Vita. Bibliography: p. 92-93.

Legal reasoning is a method that is applied by legal practitioners to make legal decisions. For a scenario, legal reasoning requires not only the facts of the scenario but also the legal rules to be enforced within it. Formal logic has long been used for reasoning tasks in many domains. Deontic logic is a logic which is often used to formalise legal scenarios with its built-in notions of obligation, permission and prohibition. Within the legal domain, it is important to recognise that there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with not only the notion of defeasibility, which allows for reasoning about exceptions, but a stronger notion of typicality which is based on defeasibility. KLM-style defeasible reasoning introduced by Kraus, Lehmann and Magidor (KLM), is a logic system that employs defeasibility while a logic that serves the same role for the stronger notion of typicality is Propositional Typicality Logic (PTL). Deontic paradoxes are often used to examine deontic logic systems as the scenarios arising from the paradoxes' structures produce undesirable results when desirable deontic properties are applied to the scenarios. This is despite the various scenarios themselves seeming intuitive. This dissertation shows that KLM-style defeasible reasoning and PTL are both effective when applied to the analysis of the deontic paradoxes. We first present the background information which comprises propositional logic, which forms the foundation for the other logic systems, as well as the background of KLM-style defeasible reasoning, deontic logic and PTL. We outline the paradoxes along with their issues within the presentation of deontic logic. We then show that for each of the two logic systems we can intuitively translate the paradoxes, satisfy many of the desirable deontic properties and produce reasonable solutions to the issues resulting from the paradoxes.

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In this work, Kurt Holukoff examines three formal approaches to representing valid inferences in reasoning regarding obligation and its cognates: deontic logic. He argues that an appropriate formalization of deontic logic should take genuine moral dilemmas seriously, be capable of representing trumping-like reasoning, and not make the naturalistic fallacy valid as a matter of logic. The three systems he investigates are, the Standard Deontic logic, a Relevant Deontic logic, and Schotch and Jennings’ multiple moral accessibility relations Deontic logic. The Standard Deontic logic has seemingly insurmountable problems representing both fruitful reasoning from an inconsistent set of obligations and trumping-like reasoning. Moreover, the naturalistic fallacy is valid in the Standard Deontic logic. The Relevant deontic logic that the author examines is capable of representing fruitful reasoning from an inconsistent set of obligations and does not make valid the naturalistic fallacy. However, the author argues that the Relevant deontic logic needs some revisions in order to represent trumping-like reasoning. Likewise, the author finds that Schotch and Jennings’ Deontic logic is capable of representing fruitful reasoning from an inconsistent set of obligations. However, in order to represent trumping-like reasoning, revisions to Schotch and Jennings’ Deontic logic are apparently required. Similar revisions are seemingly required to block the naturalistic fallacy, which is otherwise valid in Schotch and Jennings’ original system.

In this work, Kurt Holukoff examines three formal approaches to representing valid inferences in reasoning regarding obligation and its cognates: deontic logic. He argues that an appropriate formalization of deontic logic should take genuine moral dilemmas seriously, be capable of representing trumping-like reasoning, and not make the naturalistic fallacy valid as a matter of logic. The three systems he investigates are, the Standard Deontic logic, a Relevant Deontic logic, and Schotch and Jennings’ multiple moral accessibility relations Deontic logic. The Standard Deontic logic has seemingly insurmountable problems representing both fruitful reasoning from an inconsistent set of obligations and trumping-like reasoning. Moreover, the naturalistic fallacy is valid in the Standard Deontic logic. The Relevant deontic logic that the author examines is capable of representing fruitful reasoning from an inconsistent set of obligations and does not make valid the naturalistic fallacy. However, the author argues that the Relevant deontic logic needs some revisions in order to represent trumping-like reasoning. Likewise, the author finds that Schotch and Jennings’ Deontic logic is capable of representing fruitful reasoning from an inconsistent set of obligations. However, in order to represent trumping-like reasoning, revisions to Schotch and Jennings’ Deontic logic are apparently required. Similar revisions are seemingly required to block the naturalistic fallacy, which is otherwise valid in Schotch and Jennings’ original system.

In a recent paper, Bentzen proposes a semantically characterised logic called Action Type Deontic Logic, where normative concepts are applied to action expressions, rather than propositional statements. The logic offers solutions to many of the paradoxes of deontic logic. In particular, Bentzen's semantics solves many puzzles involving the interaction of permission with conjunction and disjunction. One of the reasons for these positive results is the assumption that agents always act according to norm. This assumption means that only agents with ideal behaviour are modelled; there is no possibility for norm-violation. In this thesis, proof techniques and decision procedures for Action Type Deontic Logic in the style of semantic tableau are investigated, and soundness, completeness and termination results are obtained. In order to account for the possibility of norm-violation, a new semantics based on a generalisation of Action Type Deontic Logic models is proposed. The new semantics keeps the possibility of norm-violation open, while many of the virtues of Action Type Deontic Logic remain.

In this thesis, the main focus is on deontic logic as a tool for formal representation of moral reasoning in natural language. The simple standard system of deontic logic (SDL), i.e. the minimal Kripkean modal logic extended with the deontic axiom, stating that necessity (interpreted as obligation) implies possibility (interpreted as permission), has often been considered inadequate for this aim, due to different problems, e.g. the so-called deontic paradoxes. A general survey of deontic logic and the problems with SDL is made in chapter 1. In chapter 2, a system denoted Classical Deontic-Modal logic (CDM1) is defined. In this system, there is a primary obligation operator indexed to sets of possible worlds, and a secondary requirement operator, defined in terms of strictly necessary conditions for fulfilling an obligation. This secondary operator has most of the properties of the necessity operator in SDL. In chapters 3 and 4, it is argued that CDM1 is able to handle the SDL problems presented in chapter 1 in an adequate way, and the treatment of these problems in CDM1 is also compared with their treatment in some other well-known deontic systems. In chapter 5, it is argued that even though the problems related to quantification in modal contexts are relevant to deontic logic, these issues are not specific to deontic logic. In chapter 6, the relations between some controversial features of moral reasoning, such as moral dilemmas and “non-standard” deontic categories like supererogation, and deontic logic are discussed. It is shown how CDM1 can be modified in order to accommodate these features.

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Thesis (Ph. D.)--Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

The purpose of this paper is to make a suggestion to deontic logic: Respect Hume\'s Law, the answer to the is-ought problem that says that all ought-talk is completely cut off from is-talk. Most deontic logicians have sought another solution: Namely, the solution that says that we can bridge the is-ought gap. Thus, a century\'s worth of research into these normative systems of logic has lead to many attempts at doing just that. At the same time, the field of deontic logic has come to be plagued with paradox. My argument essentially depends upon there being a substantive relation between this betrayal of Hume and the plethora of paradoxes that have appeared in two-adic (binary normative operator), one-adic (unary normative operator), and zero-adic (constant normative operator) deontic systems, expressed in the traditions of von Wright, Kripke, and Anderson, respectively. My suggestion has two motivations: First, to rid the philosophical literature of its puzzles and second, to give Hume\'s Law a proper formalization. Exploring the issues related to this project also points to the idea that maybe we should re-engineer (e.g., further generalize) our classical calculus, which might involve the adoption of many-valued logics somewhere down the line. / Master of Arts